Isn't it time you went in?

[Push 0]

If you spin the barrel each time, then yes, this is similar to skydiving. All of these results are isomorphic, of course, since it doesn't matter what the process is, only the numbers make any difference. If you do not spin the barrel, then of course it is nothing like skydiving.

And I agree with the second paragraph as well. Skydives are dependent events in the sense that your skill grows as you gain jumps.

-- Toggle Whippin' Yahoo
Skydiving is easy. All you have to do is relax while plummetting at 120 mph from 10,000' with nothing but some nylon and webbing to save you.

[Push 0]

Quote

I can see you're unable to grasp the mathematics being used here

You do realize you're talking to a professional mathematician, right?

I was pointing out the differences between jumping 25,000 times and pulling the trigger 25,000 times since you did not make it explicit that the barrel is spun after every attempt in that post.

Quote

(assuming the barrel was re-spun),

This is an important assumption. What you did not understand is that I was pointing out how important this assumption is.

I'm going to make one more attempt to explain to you why you are wrong. Since it doesn't look like you're interested in understanding why you're wrong, and are more interested in convincing me that you have found a way to disprove all of statistics, I have little hope of succeeding. I am going to analyze your version of Russian Roulette.

First, I have to right this confusion of yours:

Quote

I can use the law of averages since the 'group' in question is the aggregate of skydives recorded used to calculate the odds of experiencing a double malfunction.

This is true. However, it has no bearing on an individual skydiver. The law of averages says that if all the skydivers in the world were to make infinitely many jumps, then the ratio of DMals to total jumps would be 1/25,000. It makes a difference to an individual only if that individual is the only skydiver on the planet, and even then it doesn't really make very much difference, because he needs to make infinitely many jumps. The law of averages is really besides the point in Gambler's Fallacy, so I'm not going to spend any more time on it. I only repeat what I said, if you find yourself using it you are confused. Since I've been doing mathematics for years, I think you should listen.

Now, since you insist on being mathematical, I am going to analyze the situation you describe formally. If it makes this more difficult to follow, so be it.

Let A(n) = (24,999/25,000)^n. This is the probability of me staying alive after playing the next n times. As we can clearly see, A(n) -> 0 as n -> infinity, as you say.

Let D(n) = 1 - A(n). This is the probability of me dying. Calculating this probability without using A(n) is annoying and will require summation, because the process terminates after one success, so I'm not going to do it. It would be a good exercise in simple statistics, so I encourage you to work it out on your own.

Proof of you being wrong: The probability of me dying within 25,000 attempts is D(25,000) = 1 - A(25,000) = 1 - (24,999/25,000)^25,000 =/= 1. QED. Notice that it's pretty close to 1, but regardless it is not equal 1. Yes, believe it or not, the proof is this simple.

Explanation of why you are wrong: You do not understand the process. D(n) is the probability of me dying with the next n attempts. Read this sentence very very carefully, and think very carefully about the word "next" and what it means. I will illustrate for the third time, this time with this formalism.

Example: I am playing this Russian Roulette. I pick up the gun, put it to my forehead and fire. I do not die. What is the probability now of me dying by my 25,000th attempt? What is the probability of me dying by my 25,001st attempt? What if I make 1000 attempts? What is the probability of me dying by my 25,000th attempt? On what attempt is my probability of death equal to D(25,000)?

Answer: After one attempt - D(24,999). D(25,000).
After 1000 attempts - D(25,000 - 1000) = D(24,000). 25,000 + 1000 = 26,000.

Think very hard on the answers to these questions, then go back and read all of my explanations. If you still do not understand, go back and read it again. Accept that you did not just disprove the entire body of human knowledge, and as soon as you realize this, the faster you will understand this fallacy.

If after all this you will still insist on being right, then I have nothing further to say. I cannot make this fallacy any clearer for you. I've led you to the water three times now. It's up to you to drink it

-- Toggle Whippin' Yahoo
Skydiving is easy. All you have to do is relax while plummetting at 120 mph from 10,000' with nothing but some nylon and webbing to save you.

[Skylark 0]

Quote

Let's say the chance of breaking the ankle is 1 in 500 on any one jump.

What you are asking now is:

- What is my chance of breaking my ankle once if I jump 1 time?

- What is my chance of breaking my ankle once if I jump 25,000 times?

I would wager that a person who has done 25,000 jumps is more likely to have broken an ankle at some stage than a person who has done only one jump, simply because they are giving themselves more opportunities to hit that one chance in 500.

However, The question that opened the thread was:

- What is my chance of breaking my ankle on jump number 1?

- What is my chance of breaking my ankle on jump number 25,001 if I haven't broken it before that?

inter alia, The chance is equal for both: a 1-in-500 chance

Yes, I agree. But if someone has 25,000 jumps and still hasn't broken their ankle, they will have a higher probability of braking it on their next jump than someone who only has, say, 10 jumps. This is because the odds say that, on average, the person with only 10 jumps shouldn't break his ankle until he reaches 500 jumps, but the person with 25,000 jumps is long overdue for breaking his ankle, otherwise he is 'defeating' the odds.

havehe 'should' have broken his ankle many times before. I

"Into the dangerous world I leapt..." William Blake, Songs of Experience

[jones32 0]

[It doesn't matter how experienced you are or how well you pack, or how good your rig is. ]***
I have been following this post and the way I see it is you have a 1 in 25k chance of a double mal. If you jumped the same rig for 25k jumps, and did not have it repacked or inspected or used it in those 25k jumps, I think yes your chances would increase with every jump but after you use your reserve or have it repacked or buy a new rig whatever the case may be. Your chances would be reset to 1 in 25k. Just as your example with the russian roulette thing if you spun the barrel one time then pulled the trigger for 25k and never spun the barrel again then yes your chances are greater that you would hit the bullet before 25. If you was on 24999 then don't pull that trigger next time. But every time you spin the barrel it just reset you chances to 1 in 25k again.
But since you have you reserve repacked, buy new gear, new reserve, etc, etc, then you chances are always 1-25k that you will have a double mal.
and the Russian roulette thing is a bad example because you have little chance of stopping the bullet or moving out of the way. You can survive a double mal. If it is a line over and you have a hook knife with you the cut the line that is over the front of your reserve and bingo your saved. There is no way to know what your malfunction will be but you can be prepared for it. I treat every jump as i could have a malfunction and go through my emergancy procedurs and what i would do if it happened. So bottom line is be prepared! know that you have a 1in 25k chance that you are going to have a double mal. But hope it is not your day! Pay for whoever is unlucky enough that day to have one!
THIS IS JUST MY TWO CENT WORTH!

[Liemberg 0]

The fallacy in your thinking is that you forget to spin the wheel after every time you pull the trigger. If russian roulette was as rewarding as skydiving AND you could spin the wheel after every trigger-action, I know what i would do if the chances were equal.
Another thing you tend to forget that after a couple of jumps you (supposedly) become better at guessing which chamber holds the bullet and how to spin the wheel...

"Whoever in discussion adduces authority uses not intellect but memory." - Leonardo da Vinci
A thousand words...

[Push 0]

This argument only proves a point I've been making on some other threads. Amateurs should not attempt to make statements about technical fields, whether it be medicine or mathematics. They will inevitably get hopelessly confused.

To anyone reading this thread:

The probability of you dying does not increase with your jump numbers. As you skydive, the probability varies greatly because of a number of factors that are unrelated to the math. Still, it does not increase as you jump more. The law of averages has nothing to do with one particular individual, do not let the argument from the law of averages persuade you.

I am a mathematician. Skylark is clearly not. Please, listen to experience and focus on the important factors that could kill you, and not the law of averages.

-- Toggle Whippin' Yahoo
Skydiving is easy. All you have to do is relax while plummetting at 120 mph from 10,000' with nothing but some nylon and webbing to save you.

[rehmwa 2]

Hey Push - now try to explain to Skylark the difference between confidence intervals and prediction intervals. It's funny to watch their confused faces and cocked heads.

We had PhDs argue at work about the wrong read on the classic Monte Hall simulation and they wouldn't get it. Stats is intuitive to only some of the population. Of the rest, some will learn, of the remaining, they will 'refuse' to get it. Slarks last post proves it as it's 'exactly' incorrect.

I stop strying after about three turns.

edit: Unless he's just being purposely wrong to play games and push buttons. Then, that is really funny and I can appreciate the humor. Pushing peoples buttons is a lost art form.

...
Driving is a one dimensional activity - a monkey can do it - being proud of your driving abilities is like being proud of being able to put on pants

[Skylark 0]

Ok, a test for the 'mathematicians' to see how much they understand probability

You turn your back and ask someone to place 3 emtpy cups upside down and to place a ball under one of the cups.

You turn to face the cups. Now, two of those cups MUST be empty and one of them must hide the ball, correct? You place your hand on one of the cups at random. Now, whichever cup you choose, of the remaining two cups, at least one must be empty. With me so far? Good. You ask the person to remove the empty cup (whichever it is) and you remove your hand from the cup you chose, leaving you with two cups on the table.

So, you are left with two cups on the table, one hides the ball and one is empty. You still obviously have no idea which cup is hiding the ball and which is empty. Two cups, one with the ball, one empty. Heads or Tails, 50:50, 1/2 etc.

You are now asked to guess which cup hides the ball. You decide to choose the cup you originally placed your hand on right at the start of the game when there were 3 cups on the table. What are the odds that this cup is hiding the ball? Remember there are only 2 cups on the table, one hides the ball, one is empty.

"Into the dangerous world I leapt..." William Blake, Songs of Experience

[rehmwa 2]

That is the classic Monte Hall simulation I mentioned above. There's about 30 threads on it. Your odds of picking the ball are 1/3 if you stick.

But only because the odds were calculated at the time the pick was originally made.

You are confusing stats associated with pick and remove rather than "Pick and replace". It's normal and lots of intelligent people do it.

If you truly believe that the odds are 50/50, go ahead and run every single possibility (there are 9 - you can pick any of the three, and the ball can be under any of the three) and see for yourself.

It's not extendable to this example if that's where you are going.

I already had my three attempts earlier. I'm not getting sucked in to more of the same. Go back to where I mentioned to one of the guys about a bag of marbles and read that.

good luck

edit: I really do think you were just playing with Push and you actually do agree,

...
Driving is a one dimensional activity - a monkey can do it - being proud of your driving abilities is like being proud of being able to put on pants

[Skylark 0]

I obviously am aware that the odds are not 50:50. I was merely seeing if you were aware. But I digress.

"Into the dangerous world I leapt..." William Blake, Songs of Experience

[rehmwa 2]

Digression is the spice of life. Or at least these forums.

...
Driving is a one dimensional activity - a monkey can do it - being proud of your driving abilities is like being proud of being able to put on pants

[thelem 0]

Lets come back to the coins.

Someone mentioned earlier that if you tossed a coin 600 times and got 600 heads, then on toss 601 there would still be a 50/50 chance of getting heads on the next toss. You said you thought there would be something wrong with the coin if toss 601 was not a tail.

If I work through the first few tosses, hopefully you can see the theory will go on forever. We will keep tossing the coin until it we get tails.

On the first toss, there is a 50/50 (or 0.5 out of 1) chance of getting a head, so:
H = 0.5
T = 0.5

On the second toss, there is still a 50/50 chance of getting a head, so:
HH = 0.5 * 0.5 = 0.25
HT = 0.5 * 0.5 = 0.25
T = 0.5
Total probability of throwing tails so far = 0.5 + 0.25 = 0.75

Third toss, still a 0.5 chance:
HHH = 0.25 * 0.5 = 0.125
HHT = 0.25 * 0.5 = 0.125
Tail thrown already: 0.75
Total probability of tails so far: 0.75 + 0.125 = 0.875

Forth toss:
HHHH = 0.125 * 0.5 = 0.0625
HHHT = 0.125 * 0.5 = 0.0625
Tails thrown already: 0.875
Total probability of tails: 0.9375

So, we can say that after tossing the coin 4 times, there is a 93.75% chance that we will have thrown at least one tails, but there is still a 6.25% chance that we will have thrown only heads.

As you keep throwing the coins, the chance that you will have thrown a tail AT SOME POINT keeps increasing, but the chance of throwing a tail next time stays the same.

FYI the chance of throwing 600 heads in a row is approximatly
0.000000000000000000000000000000000000
00000000000000000000000000000000000000
00000000000000000000000000000000000000
00000000000000000000000000000000000000
0000000000000000000000000000000241 : 1
(or 2.41e-181)

The probability of throwing 601 heads in a row is approximatly
0.000000000000000000000000000000000000
00000000000000000000000000000000000000
00000000000000000000000000000000000000
00000000000000000000000000000000000000
0000000000000000000000000000000120 : 1

[benny 0]

Quote

So you agree with me then? You admit that you're more likely to experience a double mal if you skydive 25,000 times, just like you're more likely to fire onto the chamber containing the bullet if you played Russian Roulette 25,000 times, but you skydive because the risks are worth it?

Now you're putting (bad) words in my mouth. Your understanding of statistics is still flawed. I wouldn't play roulette the first or the 25000th time. Risk, 1/25000 on the former or latter would be to great. I'm not taking a 1/25000th risk on my life for the adrenaline rush that hearing the click would give me.

Never go to a DZ strip show.

[RippedCord 0]

Quote

If this is correct, these guys are presumably reaching the point where, statistically, they 'should' experience a double-mal.

Innumeracy.

AMDG

[Push 0]

Quote

I really do think you were just playing with Push and you actually do agree

That's also my suspicion right now

-- Toggle Whippin' Yahoo
Skydiving is easy. All you have to do is relax while plummetting at 120 mph from 10,000' with nothing but some nylon and webbing to save you.

[freeryde13 0]

i don't know everything about everything. but if i have a 1 in one 1000 chance of winning the lottery, that doesn't mean i'm garanteed to win ever . even in a million tries. i also might win 5 times out of 5 chances.

secondly, i don't see a double mal as purely chance. the main and reserve could be packed perfectly every time.

statistics one thing to consider regaurding safety, but certainly not the only or even the main thing to consider.

all of this of course being only my humble opinion.

_________________________________________

people see me as a challenge to their balance

[Liemberg 0]

Quote

Innumeracy.

Innumeracy ?
(After all, what are computers for...)

"Whoever in discussion adduces authority uses not intellect but memory." - Leonardo da Vinci
A thousand words...

[KolinskyDC 0]

Wow....I have such a headache after reading this post...LOL!!

Quote

Let me explain by getting you to answer the question. If you were forced to play Russian Roulette once, with a 25,000 barrel handgun, but were also given the choice of playing it 25,000 times (assuming the barrel was re-spun), which would you choose? If what you are saying is correct, that the probability of being 'unlucky' is 25,000 to 1 on the first attempt and also 25,000 to 1 on the 25,000 attempt, then presumably you wouldn't have a problem with playing it 25,000 times because, according to you the odds are exactly the same.

If I was being forced, obviously I (as well as everyone else) would choose to pull once, but with skydiving I would choose jumping 25,000 times instead of just once. This does not mean that the odds are changed at all, it just means, skydiving gives pleasure and putting a gun to your head does not, but with every jump or every pull of the trigger the odds remain the same.

The two scenarios really are not equal if you think about it though. A better scenario would be to ask, if there were 25,000 rigs placed in front of you and inside one of those rigs was a double mal and you had to choose a random rig and jump it, then have the rig re-packed and mixed back in with the other 24,999 rigs then had to pick randomly again and jump, would you jump once or 25,000 times?

Quote

But nobody would risk playing it again if they didn't have to, if they survived the first trigger pull. The reason being that, despite the barrel being re-spun, they are increasing their chances of striking unlucky by continuing to play.

Let's get this clear, the reason is not because the chances increase, it is because no-one wants to risk getting shot in the head for nothing whether it be 1 time or 1,000 times.

Melissa

"May the best of your past be the worst of your future"

[chuckinatlanta 0]

my apologies, ive only read the first page.

I have never taken a statistics class nor am I very good at math. Even so, I can visualize this and Skylark is wrong. Like somone said- every skydive is its own event and every time there is a 'roll of the dice" that has nothing to do with the previous jump.


this all makes complete sense to me.


no..someones time is not necessarily up.

now, you COULD be surprised at the fact that someone has not had a double mal after reviewing all his jumps but that has nothing to do with probability for the next jump.

hypothetically you could flip a coin and beat 50/50 odds for eternity and get heads every single time. the probibility that will happen is just laughable but it CAN happen.

[billvon 2,400]

I think everyone has made their points; it's time to move on to another thread.

[BlindBrick 0]

Quote

i don't know everything about everything. but if i have a 1 in one 1000 chance of winning the lottery, that doesn't mean i'm garanteed to win ever . even in a million tries. i also might win 5 times out of 5 chances.

Reminds me of a news item I saw back in the '90's. Seems some state's lotto machien picked the exact same numbers two days in a row.

-Blind

"If you end up in an alligator's jaws, naked, you probably did something to deserve it."

[goose491 0]

Quote

Digression is the spice of life. Or at least these forums.

BOOBIES!!!



Wait Billvon, I have a question.

What are the odds of me breaking my ankle if I drink three cups prior to playing Russian Roulette whilst skydiving and haven't yet lost my marbles in over 25,000 jumps?

My Karma ran over my Dogma!!!

[PhillyKev 0]

The fundamental confusion here is what is skylark asking?

Does someone who makes 25000 skydives over their life time have a higher probability of having a double mal than someone who only makes one?

YES

Does someone who has made 24,999 skydives have a higher probability of having a mal on their next skydive than someone who is going to make their first?

NO

Skylark keeps switching back and forth between looking at single events and a series of events. The more times an event is repeated, the closer it gets to its probabiliy when looking at THE ENTIRE SERIES OF EVENTS. But you cannot say that after completing a series of events that the probability has changed for the next single occurence.

[velo90 0]

But... if someone plans to make 25,000 skydives, and 1 in 25,000 end with a double-mal, they only have a 63% chance of having a double-mal in those 25,000 jumps.
That does not change the fact that in each single jump the chances are the same, namely 1 in 25,000.

Dave

[Tonto 1]

I had my double mal and sorted it. Glad it wasn't a total.

I should be fine for a while now...

t

It's the year of the Pig.